IMO 2010 Shortlist C3

2500 chess kings have to be placed on a 100 100 chessboard so that (i) no king can capture any other one (i.e. no two k...

IMO 2010 Shortlist C3

Category: Combinatorics

Problem

2500 chess kings have to be placed on a 100 100 chessboard so that (i) no king can capture any other one (i.e. no two kings are placed in two squares sharing a common vertex); (ii) each row and each column contains exactly 25 kings. Find the number of such arrangements. (Two arrangements differing by rotation or sym- metry are supposed to be different.) (Russia)